A160225 Numerator of Hermite(n, 2/29).

1, 4, -1666, -20120, 8326156, 168671984, -69348284024, -1979630798624, 808588172904080, 29872264717900864, -12120918702550359584, -550935167365293970816, 222057497165125577139904, 12008305406761595815509760, -4807476011385589486479101824

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Formula

From G. C. Greubel, Jul 12 2018: (Start)

a(n) = 29^n * Hermite(n, 2/29).

E.g.f.: exp(4*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 4/29, -1666/841, -20120/24389, 8326156/707281

Mathematica

Table[Numerator[HermiteH[n, 2/29]], {n, 0, 15}] (* Wesley Ivan Hurt, Feb 25 2014 *)
Table[29^n*HermiteH[n, 2/29], {n, 0, 30}] (* G. C. Greubel, Jul 12 2018~ *)

Prog

(PARI) a(n)=numerator(polhermite(n, 2/29)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018

Crossrefs

Cf. A009973 (denominators).

Sequence in context: A361449 A265661 A280793 * A316484 A278794 A141090

Adjacent sequences: A160222 A160223 A160224 * A160226 A160227 A160228

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved